How about designing interference-experiments where the design of the experiments itself represents algorithmical or mathematical problems that are coded in a way that the solution to that problem is interference = “true” and no interference = “false” as a result?

These results would be acquired instantaneously because the algorithm would not be processed step by step as with classical computers. If the design was changed on the run - thereby representing another problem - the solution would even be acquired faster than the quanta going through the apparatus as predicted by “delayed choice”-experiments.

Are there already such ideas for “quantum computers” of this kind? They would not have the problem of decoherence but on the contrary decoherence vs. no-decoherence would be their solution set of the problems represented by the (flexible) experimental design.

Does this make sense?

EDIT: Perhaps my question is not formulated well - perhaps I shouldn't call it "quantum computer". My point is that any configuration with these double slit experiments - no matter how complicated - instantly shows an interference pattern when there is any chance of determining the way the photons took. My idea is to encode some kind of calculation or logical problem in this configuration and instantly find the answer by looking at the outcome: interference = “yes” and no interference = “no” –

2 Answers
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Here is my understanding of what you are asking (and I believe it is a little different to Lubos's interpretation, so our answers will differ): Can you build a computer that uses the interference effects to perform computation, where you use the presence of light in a particular place to represent 1 and no light to represent 0?

The answer is yes, though with certain caveats. First let me note that there is something already called a quantum computer which exploits quantum effects to outperform normal (classical) computers. Classical computation is a special case of quantum computation, so a quantum computer can do everything a classical computer can do, but the converse is not true.

If you have single photon detectors, you can use the interference effects of a network of beam splitters and phase plates together with the detectors to create a universal quantum computer. This is something called linear-optics quantum computing or LOQC. Perhaps the best known scheme is the KLM proposal, due to Knill, Laflamme and Milburn.

Now the caveats: you need to have a fixed finite number of photons, and you need to adapt the network based on earlier measurement results. This adaptive feed-forward is quite difficult to achieve in practice, though not impossible, and computation with such a setup has been demonstrated.

A further interpretation of the question is whether it is sufficient to use such a linear network, but only make measurements at the end. This is an open question, though there is strong evidence that such a device is not efficiently simulable by a classical computer (see this paper by Scott Aaronson). It is however not yet known whether you can implement universal classical or quantum computing on such a device.

Note: In the case of these examples there is always interference, and it is simply measuring which pattern you get that gives the answer. However it is possible to break the schemes so that you get interference for the answer 0, and so the photon always comes in a particular mode, where as for 1 the coherence is deliberately destroyed, so you get the photon randomly in one of several modes. This is no longer deterministic computation, but can be made arbitrarily close to deterministic. It is worth noting,however,that theres no advantage to this and its more sensible to keep everything coherent
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Joe FitzsimonsJan 20 '11 at 16:13

no, you cannot represent a quantum bit in a quantum computer by "coherence vs decoherence" because any decoherence means that the computer ceased to be a quantum computer. So once the first "zero" would appear in your computer, you would start to get incorrect results.

Your answer to kakemonsteret that you may "detect interference by seeing an interference pattern" is a misunderstanding what should be seen and what is seen in quantum mechanics. In quantum mechanics, one only sees an interference pattern if the very same experiment is repeated many times. So this would be needed to determine the value of the qubit - which would also become a classical bit - for every operation, so the number of repetitions would grow exponentially with the number of operations needed to perform the quantum algorithm.

It just doesn't work. Decoherence may only occur at the end of the calculation in a quantum computer - when the result is being read. Any decoherence before that means that the quantum computer has broken down. Moreover, "coherence vs decoherence" is not really a quantum bit to start with - because you can't create linear superpositions of these two "states" with controllable phases - decoherence always has an undetermined phase.

Perhaps my question is not formulated well - perhaps I shouldn't call it "quantum computer". My point is that any configuration with these double slit experiments - no matter how complicated - instantly shows an interference pattern when there is any chance of determining the way the photons took. My idea is to encode some kind of calculation or logical problem in this configuration and instantly find the answer by looking at the outcome: interference = “yes” and no interference = “no”
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vonjdJan 20 '11 at 14:32

Fine, vonjd, you may call it whatever you want. I was just trying to explain that it's not a quantum computer, and because it's not a quantum computer, it's not useful. You won't get the exponential speeding that quantum computers can do, you won't be able to crack the codes and factorize large products of primes. In fact, it won't be usable as a classical computer, either - because of the stochastic component.
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Luboš MotlJan 20 '11 at 15:04

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@vonjd: You won't see the pattern instantly, you are limited by the finite speed of light which means it takes a finite amount of time for the light to pass through the network, which will be proportional to the depth of the network.
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Joe FitzsimonsJan 20 '11 at 15:54